Uniform Random Covering Problems
Motivated by the random covering problem and the study of Dirichlet uniform approximable numbers, we investigate the uniform random covering problem. Precisely, consider an i.i.d. sequence ω = (ωn)n≥1 uniformly distributed on the unit circle &x1D54B; and a sequence (rn)n≥1 of positive real numbers with limit 0. We investigate the size of the random set U(ω) := {y ∈ &x1D54B;: ∀N ≫ 1, ∃n ≤ N